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Thread Subject:
Numerical Integration

Subject: Numerical Integration

From: KAMAL ABAZA

Date: 8 May, 2010 17:18:04

Message: 1 of 4

Hello Guys,
I'm Having a problem at integration a function on matlab the function is as follow :
Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ "
Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication"
λ is vector of eigen values KNOWN (the whole vector is available)
E is also known
ω is a variable unknown and I want to integrate on .
hope that the equations are clear enough
how can integrate this function numerically ???? !!!!
thanks in Advance

Subject: Numerical Integration

From: Roger Stafford

Date: 8 May, 2010 20:13:05

Message: 2 of 4

"KAMAL ABAZA" <abaza_kamal@yahoo.com> wrote in message <hs46cc$ndc$1@fred.mathworks.com>...
> Hello Guys,
> I'm Having a problem at integration a function on matlab the function is as follow :
> Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ "
> Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication"
> λ is vector of eigen values KNOWN (the whole vector is available)
> E is also known
> ω is a variable unknown and I want to integrate on .
> hope that the equations are clear enough
> how can integrate this function numerically ???? !!!!
> thanks in Advance
- - - - - - - -
  Use 'quadgk', which accepts infinite limits of integration. You will need to write a function for your integrand which accepts vector arguments, and it will need to accept the known parameters E and vector lambda.

  I assume that some of the eigenvalues in lambda are complex-valued in appropriate ways. Otherwise the function would not be integrable.

Roger Stafford

Subject: Numerical Integration

From: Bruno Luong

Date: 8 May, 2010 21:18:07

Message: 3 of 4

"KAMAL ABAZA" <abaza_kamal@yahoo.com> wrote in message <hs46cc$ndc$1@fred.mathworks.com>...
> Hello Guys,
> I'm Having a problem at integration a function on matlab the function is as follow :
> Integral = ∫[ϕ(ω) e^(-jωE) dω] " integration from -∞ to +∞ "
> Where: ϕ(ω)=∏[(1-j2ωλ(i))]^(-1) "multiplication"
> λ is vector of eigen values KNOWN (the whole vector is available)
> E is also known
> ω is a variable unknown and I want to integrate on .
> hope that the equations are clear enough
> how can integrate this function numerically ???? !!!!

It seems like you can use Residue Theorem to compute such thing almost by hand.

Bruno

Subject: Numerical Integration

From: Roger Stafford

Date: 8 May, 2010 21:41:05

Message: 4 of 4

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hs4kef$c9p$1@fred.mathworks.com>...
> It seems like you can use Residue Theorem to compute such thing almost by hand.
>
> Bruno

  I agree, Bruno!

Roger Stafford

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